Correct Answer: $\frac{3}{5}$

Solution : Given: $\sec\  A + \tan \ A = 3$ ---(1)
We know, $\sec^2A-\tan^2A =1$
⇒ $(\sec\  A - \tan \ A)(\sec \ A + \tan\ A) = 1$
⇒ $(\sec\  A - \tan\  A) = \frac{1}{3}$ ---(2)
On adding the equations 1 and 2, we get,
$(\sec \ A + \tan \ A) + (sec \ A - \tan \ A) = 3+\frac{1}{3}$
⇒ $2\sec\  A = \frac{10}{3}$
$\therefore \sec \ A = \frac{5}{3}$
The value of $\cos \ A = \frac{1}{\sec \ A}=\frac{3}{5}$
Hence, the correct answer is $\frac{3}{5}$.